Convert Logarithm to Exponent - From Decimal (Level 1)

This math topic focuses on converting logarithmic expressions to their equivalent exponential forms, specifically dealing with logarithms of decimal values. The problems require understanding the relationship between logarithms and exponents, especially in cases where both the base and the exponent are decimals. Each question presents a logarithmic equation that must be transformed into the correct exponential form, with several options provided for students to select the correct conversion. This practice helps to deepen understanding of logarithmic functions and their applications in various mathematical contexts.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Logarithms - Convert Logarithm to Exponent - From Decimal Worksheet

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Logarithms - Convert Logarithm to Exponent - From Decimal
1
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 4 16 = 2
a A LaTex expression showing 2 to the power of 4 = 16
b A LaTex expression showing 4 to the power of 2 = 16
c A LaTex expression showing 16 to the power of 4 = 2
2
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 8 14,263.1 = 4.6
a A LaTex expression showing 14,263.1 to the power of 4.6 = 8
b A LaTex expression showing 4.6 to the power of 14,263.1 = 8
c A LaTex expression showing 14,263.1 to the power of 8 = 4.6
d A LaTex expression showing 8 to the power of 4.6 = 14,263.1
3
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 7 2,916.77 = 4.1
a A LaTex expression showing 4.1 to the power of 7 = 2,916.77
b A LaTex expression showing 4.1 to the power of 2,916.77 = 7
c A LaTex expression showing 2,916.77 to the power of 4.1 = 7
d A LaTex expression showing 7 to the power of 4.1 = 2,916.77
4
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 8 147.03 = 2.4
a A LaTex expression showing 147.03 to the power of 8 = 2.4
b A LaTex expression showing 2.4 to the power of 8 = 147.03
c A LaTex expression showing 2.4 to the power of 147.03 = 8
d A LaTex expression showing 8 to the power of 2.4 = 147.03
5
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 5 106.42 = 2.9
a A LaTex expression showing 106.42 to the power of 5 = 2.9
b A LaTex expression showing 2.9 to the power of 106.42 = 5
c A LaTex expression showing 5 to the power of 2.9 = 106.42
d A LaTex expression showing 2.9 to the power of 5 = 106.42
6
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 6 5,434.08 = 4.8
a A LaTex expression showing 4.8 to the power of 6 = 5,434.08
b A LaTex expression showing 6 to the power of 4.8 = 5,434.08
c A LaTex expression showing 5,434.08 to the power of 6 = 4.8
d A LaTex expression showing 5,434.08 to the power of 4.8 = 6
7
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 4 24.25 = 2.3
a A LaTex expression showing 2.3 to the power of 24.25 = 4
b A LaTex expression showing 4 to the power of 2.3 = 24.25
c A LaTex expression showing 24.25 to the power of 2.3 = 4
d A LaTex expression showing 2.3 to the power of 4 = 24.25
e A LaTex expression showing 24.25 to the power of 4 = 2.3
8
Convert the given logarithm to the equivalent in exponent form
A LaTex expression showing \log sub 9 47,401.09 = 4.9
a A LaTex expression showing 9 to the power of 4.9 = 47,401.09
b A LaTex expression showing 4.9 to the power of 47,401.09 = 9
c A LaTex expression showing 47,401.09 to the power of 4.9 = 9
d A LaTex expression showing 47,401.09 to the power of 9 = 4.9