Rewrite the following expression as a single logarithm with coefficient 1.3log5 uv2w3
To rewrite the expression 1
To rewrite the expression 1.3log5 uv^2w^3 as a single logarithm with a coefficient of 1, we can use the logarithmic property which states that for any positive number ‘a’ and real numbers ‘x’ and ‘y’, the logarithm of ‘a’ raised to the power of ‘x’ plus the logarithm of ‘a’ raised to the power of ‘y’ is equal to the logarithm of ‘a’ raised to the power of ‘x’ times ‘y’. Based on this property, we can rewrite the expression as:
1.3log5 uv^2w^3 = log5 (uv^2w^3)^1.3
Now, let’s simplify further by using another logarithmic property which states that for any positive number ‘a’ and real numbers ‘x’ and ‘y’, the logarithm of ‘a’ raised to the power of ‘x’ is equal to ‘x’ multiplied by the logarithm of ‘a’. Using this property, we can rewrite the expression as:
log5 (uv^2w^3)^1.3 = 1.3 * log5 (uv^2w^3)
Therefore, the expression 1.3log5 uv^2w^3 can be rewritten as 1.3 * log5 (uv^2w^3) with a coefficient of 1.
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